I have always struggled with the concept of spontaneous symmetry breaking. It seems to me that many others don't find it very intuitive as well, but that could be just me having difficulties with the big picture behind it.
Anyway, I would like to change it and understand this concept better, if it's possible. To be honest, without any formulas and Lagrangians, to me it just looks like this:
- Write the 'wrong' Lagrangian in which particles do not have mass,
- From experiment find out that particles actually do have mass,
- Fix the initial Lagrangian by inventing new particles and connecting them to the old particles in a way that they now have mass (part where we 'generate' mass),
- Call the Lagrangian 1. and 3. related by symmetry breaking/symmetry restauration.
So, why do 1-4? Couldn't one immediately write the 'effective' Lagrangian with all the desired masses and work with that? Why complicate if it can be simpler?